Farsighted stability of the competitive allocations in an exchange economy with indivisible goods

Farsighted house allocation

“…A coalition might well enforce a myopically not very attractive outcome (i.e., the redistribution of endowments makes some members of the blocking coalition worse off) in order to set a chain of events in motion that in the end will lead to a preferred outcome for everyone in the coalition. Following this line of thought, Kawasaki (2008) demonstrates that the set of competitive allocations coincides with the unique von Neumann-Morgenstern stable set defined in terms of a farsighted version of Wako's (1999) antisymmetric weak dominance.…”

“…Likewise, a tenant strictly prefers his own room to any room with identical characteristics -he likes to avoid moving-, while he also strictly prefers any room with distinctly better characteristics to his own. Hence, we give a farsighted characterization of the set of competitive allocations in a housing market based on strong dominance (i.e., a stronger dominance relation than the one used in Kawasaki, 2008) on a restricted preference domain. In fact, we demonstrate that this is a maximal domain.…”

“…Kawasaki (2008) shows that the set of competitive allocations coincides with the unique von Neumann-Morgenstern stable set based on a farsighted version of antisymmetric weak dominance (cf., Wako, 1999). We demonstrate that the set of competitive allocations also coincides with the unique von Neumann-Morgenstern stable set based on a farsighted version of strong dominance (cf., Roth and Postlewaite, 1977) if no individual is indifferent between his endowment and the endowment of someone else.…”

Single-payoff farsighted stable sets in strategic games with dominant punishment strategies

“…Some kinds of the stable sets with farsighted players have been well investigated in market models such as Greenberg, et al (2002), Kawasaki (2010), Klaus, et al (2010), and Mouleon, et al (2011), among others. The FSS by Ray and Vohra (2015a) also applies to the market economy models since they are frequently formulated in coalitional games.…”

“…For example, Diamantoudi and Xue (2003) for the hedonic coalition formation problem; Diamantoudi (2005) for the cartel formation problem; Diamantoudi and Sartzetakis (2015) and Benchekroun and Chaudhuri (2015) for the international environmental agreement formation problems; Page and Wooders (2009) for the network formation problem; Kawasaki (2010) and Klaus, et al (2010) for the exchange economy with indivisible goods under the weak and strong dominance relations, respectively; Klaus, et al (2011) for the roommate problem; Mouleon, et al (2011) for the two-sided matching markets, and it is extended to a more general setting by Roketskiy (2012), among others.…”